Determine if the following series converges or diverges. If it converges determine its sum.∞∑n=0 (−1)n
1 answer:
Answer: The given series neither converges nor diverges.
Step-by-step explanation: We are given to determine whether the following series converges or diverges :
If the series converges, we are to find its sum.
The given series can be written as :
We note that the given series is a geometric one with first term 1 and common ratio given by
We know that a geometric series with common ratio r converges if |r| <1 and diverges if |r| > 1.
Since |r| = 1 for the given series, so the series will neither converge nor diverge.
Thus, the given series neither converges nor diverges.
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Answer:
Bryce is wrong in step 1 because he did not distribute 3 over 5/3
Explanation
Given the steps taken by bryce as shown, we are to find where he made an error
Given the expression;
Step 1:Expand the bracket using the distributive law;
8/3 = 3c + 3(5/3)
<em>Simplify</em>
8/3 = 3c + 15/3
Step 2: Subtract 15/3 from both sides
8/3 - 15/3 = 3c+15/3-15/3
(8-15)/3 = 3c
-7/3 = 3c
Step 3: Multiply both sides by 1/3
-7/3 * 1/3 = 3c * 1/3
-7/9 = c
Swap
c = -7/9
From the calculation, we can see that Bryce is wrong in step 1 because he did not distribute 3 over 5/3 thereby making his solution incorrect